Spherical Tank Volume Calculator (Partially Filled Sphere)
By Santaji GadepatilinUpdated November 5, 2026
Storage spheres for LPG, ammonia and other pressurised liquids hold far more or less than a simple level percentage suggests, because the cross-section changes with height. This spherical tank volume calculator uses the spherical-cap formula to convert level to volume — the basis of LPG level measurement in bullets and spheres and of tank volume from level.
How to use the spherical tank volume calculator
Enter the inside diameter of the sphere and the liquid level measured from the bottom. The calculator returns the liquid volume, the full capacity and the percent filled. To find the level for a given volume, clear the level and enter the volume.
Spherical tank volume formula
V = π h² (3R − h) ÷ 3 · Vtotal = π D³ ÷ 6
Worked example
A 10 m sphere (R = 5 m) with 4 m of liquid:
- V = π × 4² × (15 − 4) ÷ 3 = 184.31 m³
- Capacity = π × 10³ ÷ 6 = 523.60 m³
- Filled = 184.31 ÷ 523.60 = 35.2% — at 40% of the level
Level-to-volume table for a 10 m sphere
| Level | Volume | % of capacity |
|---|---|---|
| 10% (1.0 m) | 14.66 m³ | 2.8% |
| 20% (2.0 m) | 54.45 m³ | 10.4% |
| 30% (3.0 m) | 113.10 m³ | 21.6% |
| 40% (4.0 m) | 184.31 m³ | 35.2% |
| 50% (5.0 m) | 261.80 m³ | 50.0% |
| 60% (6.0 m) | 339.29 m³ | 64.8% |
| 70% (7.0 m) | 410.50 m³ | 78.4% |
| 80% (8.0 m) | 469.14 m³ | 89.6% |
| 90% (9.0 m) | 508.94 m³ | 97.2% |
| 100% (10.0 m) | 523.60 m³ | 100.0% |
Notes
- Level and volume are only equal (in percent) at 0, 50% and 100%.
- For mass, multiply the volume by the liquid density at the measured temperature.
Frequently asked questions
What is the formula for a partially filled sphere?
V = π h² (3R − h) ÷ 3, where R is the radius and h the liquid depth. It is the volume of a spherical cap and holds for any level from 0 to 2R.
Why is 50% level exactly 50% volume?
A sphere is symmetrical about its equator, so half the height holds half the volume. Below and above the middle, volume changes much more slowly per unit level than in a vertical cylinder.
How full should an LPG sphere be filled?
Typically to no more than 85% of volume to leave vapour space for thermal expansion — check the local regulation and the design.
Does the calculator use inside or outside diameter?
Inside diameter. Subtract twice the wall thickness from the outside diameter for an accurate capacity.